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On the hydrodynamics of ‘slip–stick’ spheres

Published online by Cambridge University Press:  10 July 2008

JAMES W. SWAN  and
ADITYA S. KHAIR
JAMES W. SWAN
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91106, USA
ADITYA S. KHAIR
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91106, USA Department of Chemical Engineering, University of California Santa Barbara, CA 93106, USA
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Abstract

The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxén-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 606 , 10 July 2008 , pp. 115 - 132
Copyright
Copyright © Cambridge University Press 2008

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